In what ways did the Compromise of 1877 help the nation in rebuilding itself?

The answer to this question depends on what one means by "rebuilding." The Compromise, which resolved the controversy that developed as a result of contested presidential election results in Florida, Louisiana, and South Carolina. The actual terms of the "compromise" were hammered out by a commission appointed by Congress to determine the election results in those states. The decision was made to award the presidency to Rutherford B. Hayes, a Republican, rather than Samuel Tilden, a Democrat (who was only one vote shy of the majority of electoral votes needed to win.) This decision had little to do with the voting process in the states. What was at stake was the future of Reconstruction, which had already come to an end in most southern states, which had returned to Democratic (redeemer) rule. Southern Democrats struck a bargain with Republicans, agreeing to accept Hayes as President in return for an end to Reconstruction. This entailed the removal of federal troops from Southern states, as well as, for all practical purposes, the end of federal efforts to enforce civil rights for the millions of African-Americans in the South. In the decades that followed, blacks were systematically disfranchised and Jim Crow laws designed to maintain white supremacy were established. So while the Compromise of 1877 effected regional reconciliation by ending the Reconstruction era, it did so at the cost of the basic rights of African-Americans.